{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "jgy0CRgd4koZ"
   },
   "source": [
    "# Computing the expected information density in the Ergodic Information Harvesting algorithm\n",
    "This is a tutorial on how to compute the expected information density, a key element of the EIH. Once it is computed, a trajectory that balances energy expenditure with ergodicity is generated as described in the Supplement, moving the measuring or sensing system so as to gamble on the information represented by the EID through motion. \n",
    "\n",
    "Chen Chen & Malcolm MacIver & Todd Murphey\n",
    "\n",
    "August 2019"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Table of Contents\n",
    "1. [Example Description](#0.-Example-Description)\n",
    "2. [Observation Model](#2.-Observation-Model)\n",
    "3. [Likelihood](#3.-Likelihood)\n",
    "4. [Bayesian Filter](#4.-Bayesian-Filter)\n",
    "5. [Expected Information Density](#5.-Expected-Information-Density)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "***"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "CbJTvrYsBTEC"
   },
   "source": [
    "## 1. Example Description\n",
    "To start our tutorial, let's define a scenario. Imagine we have a robot equipped with a microphone capable of moving along a line. There is a stationary buzzer that generates a fixed-intensity sound located in the same space. The microphone on the robot only gives the loudness of the sound it picks up—ignoring pitch. The task here is to move the robot along the 1D axis to take measurements and use them to estimate the location of the buzzer."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "5i4_WcVx-QAD"
   },
   "source": [
    "## 2. Observation Model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "2D0Q1aLa-de7"
   },
   "source": [
    "For the sake of simplicity, let's say our robot can only move between 0 to 1. We can represent the scenario as:\n",
    "\n",
    "- A sensor (microphone), with location denoted by $x$, can move freely within 1D space $x \\in \\mathbb{X}=[0, 1]$\n",
    "- A signal source (buzzer) is fixed at a particular location within the 1D space $\\theta \\in [0, 1]$\n",
    "- The sensor's measurement of sound loudness is denoted by $V \\in \\mathbb{V} = [0, 1]$\n",
    "\n",
    "An observation model relates measured signals to random variables. The observation model, in our case, relates the measured **loudness of sound** to the **location of the sound source (buzzer)**. For example, receiving a numerical measurement of $V=0.5$ does not give us any information about where the sound source is *unless we have an observation model of our sensor*."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "colab": {
     "autoexec": {
      "startup": false,
      "wait_interval": 0
     }
    },
    "colab_type": "code",
    "id": "-jO4c2Oh4kob"
   },
   "outputs": [],
   "source": [
    "# import libraries\n",
    "import numpy as np\n",
    "import scipy as sp\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "from matplotlib.pyplot import plot\n",
    "from scipy.stats import norm, entropy, recipinvgauss\n",
    "from scipy.interpolate import interp1d\n",
    "from scipy.signal import convolve\n",
    "\n",
    "# Configure Matplotlib\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "cellView": "code",
    "colab": {
     "autoexec": {
      "startup": false,
      "wait_interval": 0
     },
     "base_uri": "https://localhost:8080/",
     "height": 361
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 699,
     "status": "ok",
     "timestamp": 1523978745920,
     "user": {
      "displayName": "Chen Chen",
      "photoUrl": "//lh6.googleusercontent.com/-WdjMoiJU9X8/AAAAAAAAAAI/AAAAAAAABR4/a7zNcVTHSAY/s50-c-k-no/photo.jpg",
      "userId": "106846184394987586128"
     },
     "user_tz": 300
    },
    "id": "Fk9RK9zp4kof",
    "outputId": "a9945d16-c44a-4309-9ba2-5ed63e88701a"
   },
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 1008x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# workspace spec\n",
    "wsResolution = 101 # resolution\n",
    "wsSamples = np.linspace(0, 1, wsResolution)\n",
    "\n",
    "# observation model\n",
    "def Upsilon(theta=0.5, sigmaM=0.1):\n",
    "    if type(theta) is float:\n",
    "        mm = norm.pdf(wsSamples,theta,sigmaM)\n",
    "        mm /= max(mm)\n",
    "    else:\n",
    "        # query multiple possible target theta\n",
    "        mm = []\n",
    "        for t in theta:\n",
    "            mm_ = norm.pdf(wsSamples,t,sigmaM)\n",
    "            mm_ /= max(mm_)\n",
    "            mm.append(mm_)\n",
    "        mm = np.array(mm)\n",
    "    return mm\n",
    "  \n",
    "# Visualize an observation model\n",
    "plt.figure(figsize=(14,5));\n",
    "plot(wsSamples, Upsilon(0.5));\n",
    "plot(wsSamples, np.tile([0.5], wsResolution))\n",
    "plt.legend((r'Observation Model Given $x = 0.5$', 'Example Measurement $V = 0.5$'), fontsize=14, loc='best')\n",
    "plt.xlabel(r'Candidate Buzzer Location ($\\theta$)', fontsize=14);\n",
    "plt.ylabel('Measurement ($V$)', fontsize=14);\n",
    "plt.title(r\"Observation Model $\\Upsilon(\\theta, x = 0.5)$\", fontsize=14);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "pep7LD8t3TAV"
   },
   "source": [
    "The plot illustrates what an observation model might look like. Specifically, this is a Gaussian observation model. For our microphone and buzzer example, the plot assumes the sensor location is fixed at $x=0.5$, and predicts the sound intensity as a function of candidate buzzer location ($\\theta$). \n",
    "\n",
    "When the buzzer's location is closer to the sensor at 0.5, we get a larger sensor reading, and the opposite happens when it is further away. Clearly, given a measurement of $V = 0.5$, the expected location of the source can be inferred from the observation model, but not uniquely. Drawing an orange line at $V=0.5$ in the same plot, we can find two possible solutions (the $\\theta$ location at which the orange line crosses the blue curve)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "sFcwXaDeVoIs"
   },
   "source": [
    "## 3. Likelihood"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "UDF2iQdZV2WL"
   },
   "source": [
    "Thus far the observation model itself has no uncertainty: if you receive a measurement $V=0.5$ as shown above, the target $\\theta$ will be in one of the two possible locations, but whichever of the two it is, it is exactly the location given by the intersection of the orange and blue curves. In other words, the resulting solutions of $\\theta$ that satistifies $\\Upsilon(\\theta, x = 0.5)=0.5$ is deterministic, though not unique. In engineered systems, one of the most common forms of uncertainty is measurement noise. Somewhere in the measurement process, either in the sensor itself or in the analog-to-digital converter we are using or something else (for example, a limited number of significant digits in the floating point numbers of the computer representing our measurements), uncertainty—often modeled as noise—will occur. In biological systems, sensory systems have a variety of uncertainty sources. In visual systems such as that of the moth tracking a flower in our study, there is motion blur (when an image passes over more than one photoreceptor acceptance angle per response time) and dark noise level (photoreceptor responses that seem like they are due to a photon but are not). In either case, instead of the sensor providing a response that matches the observation model, the sensor generates a reading that deviates from the prediction by some amount. Perhaps the simplest way to incorporate this uncertainty in the observations is with the addition of zero-mean Gaussian noise, as follows:\n",
    "$$\n",
    "V = \\Upsilon(\\theta, x) + \\epsilon\n",
    "$$\n",
    "where $\\Upsilon(\\theta, x)$ is the observation model and $\\epsilon$ represents the additive zero-mean Gaussian noise.\n",
    "\n",
    "How should this uncertainty be represented in the process of inferring the distribution over the random variable (*i.e.*, the location of the target $\\theta$) using the observation model? One method is to use a Gaussian likelihood function.\n",
    "\n",
    "### Intuition for the Likelihood Function\n",
    "The likelihood function does essentially the same operation as our example in the measurement plot of drawing a measurement line on top of the observation model to figure out where the target location is. The main difference is that the aformentioned approach assumes no uncertainty because we used only one solid line to represent a measurement. Given uncertainty, our measurement could be in the form of $V = 0.5\\pm0.1$, where 0.5 is from the deterministic observation model and 0.1 comes from uncertainty. This is equivalent to drawing a series of lines within $0.5\\pm0.1$ and using that to estimate a range of possible target locations. When the candidate buzzer location is represented by a probability density function $p(\\theta)$ instead of a single value, the likelihood function is evaluated by taking all the $\\theta$ and adding up the likelihoods of locations weighted by the likelihood of measurement $V$ given by $p(\\theta)$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "colab": {
     "autoexec": {
      "startup": false,
      "wait_interval": 0
     },
     "base_uri": "https://localhost:8080/",
     "height": 428
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 550,
     "status": "ok",
     "timestamp": 1523980067707,
     "user": {
      "displayName": "Chen Chen",
      "photoUrl": "//lh6.googleusercontent.com/-WdjMoiJU9X8/AAAAAAAAAAI/AAAAAAAABR4/a7zNcVTHSAY/s50-c-k-no/photo.jpg",
      "userId": "106846184394987586128"
     },
     "user_tz": 300
    },
    "id": "SoqAYoKD4koo",
    "outputId": "e5f07509-5e10-4a18-c35b-ca067998b7c7"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "For example:\n",
      "\n",
      "The likelihood that the buzzer is located at 0.4\n",
      "given a measurement V=0.625 at location x=0.5 is\n",
      "\tp(V = 0.625 | theta = 0.4, x = 0.5) = 0.0514\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1008x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# likelihood function\n",
    "def Pvtheta(v, theta, sigmaM=0.1, sigmaL=0.2):\n",
    "    # Compute likelihood\n",
    "    pvt = ( 1.0 / (np.sqrt(2.0*np.pi) * sigmaL) ) * np.exp( -(v - Upsilon(theta, sigmaM))**2 / (2.0 * sigmaL**2) )\n",
    "    # Normalize\n",
    "    if pvt.ndim == 1:\n",
    "        return pvt / pvt.sum()\n",
    "    else:\n",
    "        for idx in range(pvt.shape[0]):\n",
    "            pvt[idx, :] /= pvt[idx, :].sum()\n",
    "    return pvt\n",
    "\n",
    "# Visualize an example likelihood\n",
    "plt.figure(figsize=(14,5))\n",
    "plot(wsSamples, Pvtheta(0.625, 0.5))\n",
    "plt.xlabel(r'Candidate Buzzer Location ($\\theta$)', fontsize=14)\n",
    "plt.ylabel(r'Likelihood', fontsize=14)\n",
    "plt.title(r'Likelihood $p(V=0.625~|~\\theta, x=0.5)$', fontsize=14)\n",
    "\n",
    "print(\"For example:\\n\\nThe likelihood that the buzzer is located at 0.4\\n\"\n",
    "      \"given a measurement V=0.625 at location x=0.5 is\\n\"\n",
    "      f\"\\tp(V = 0.625 | theta = 0.4, x = 0.5) = {Pvtheta(0.625, 0.5)[40]:.4f}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "RJZvdgHDbw4U"
   },
   "source": [
    "## 4. Bayesian Filter"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "MOKx8LRdPJUp"
   },
   "source": [
    "### Probability Distribution, Probability Density Function (Belief), and Entropy of the Belief\n",
    "The goal of the example is to take consecutive measurements through the microphone to form an accurate estimate of the buzzer's location. Our robot's knowledge about the buzzer's location can be captured in a probability distribution. We can visualize this in the form of a probability density function (PDF) $p(\\theta)$ where $\\theta$ is the buzzer's location we are trying to estimate. The PDF is often referred to as the *belief* as it represents what the robot believes about the buzzer position for all possible candidate positions. Let's use an example to demonstrate what the belief PDF looks like and how it can be applied."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "colab": {
     "autoexec": {
      "startup": false,
      "wait_interval": 0
     },
     "base_uri": "https://localhost:8080/",
     "height": 396
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 865,
     "status": "ok",
     "timestamp": 1523992937170,
     "user": {
      "displayName": "Chen Chen",
      "photoUrl": "//lh6.googleusercontent.com/-WdjMoiJU9X8/AAAAAAAAAAI/AAAAAAAABR4/a7zNcVTHSAY/s50-c-k-no/photo.jpg",
      "userId": "106846184394987586128"
     },
     "user_tz": 300
    },
    "id": "p4ggRwP9Qysf",
    "outputId": "03ee489f-677d-4495-b759-7cc653c71146"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 2304x504 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot some PDF as example and their corresponding entropy\n",
    "priorP1 = np.ones(wsResolution)/wsResolution # An uniform \"uninformative\" PDF\n",
    "priorP3 = norm.pdf(wsSamples,0.5,0.2)        # A high-variance Gaussian PDF\n",
    "priorP4 = norm.pdf(wsSamples,0.5,0.05)       # A low-variance Gaussian PDF\n",
    "priorP1 /= priorP1.sum()\n",
    "priorP3 /= priorP3.sum()\n",
    "priorP4 /= priorP4.sum()\n",
    "\n",
    "_, (ax1, ax2) = plt.subplots(1, 2, figsize=(32,7))\n",
    "ax1.plot(wsSamples, priorP1, color='r')\n",
    "ax1.plot(wsSamples, priorP3, color='g')\n",
    "ax1.plot(wsSamples, priorP4, color='b')\n",
    "ax1.set_xlabel(r'Candidate Buzzer Position ($x$)', fontsize=14)\n",
    "ax1.set_ylabel(r'Probability', fontsize=14)\n",
    "ax1.legend(('Uniform', 'High-variance Gaussian', 'Low-variance Gaussian'), \n",
    "           fontsize=14, loc='best');\n",
    "\n",
    "ax2.barh([0,1,2], [entropy(priorP1), entropy(priorP3), entropy(priorP4)], height=0.4, \n",
    "        color=['r', 'g', 'b'])\n",
    "ax2.set_yticks([0, 1, 2])\n",
    "ax2.set_yticklabels(('Uniform', 'High-variance Gaussian', 'Low-variance Gaussian'), \n",
    "                   fontsize=12)\n",
    "ax2.invert_yaxis()\n",
    "ax2.set_xlabel(r'Entropy of PDF', fontsize=14);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "Egz5EjPMSAEX"
   },
   "source": [
    "The plot above shows three different belief PDFs. In our case, a belief is a function of candidate buzzer position as shown along the horizontal axis, with probability shown along the vertical axis. We encode knowledge of the buzzer's location through the belief. Three belief distributions are shown: \n",
    "- **Uniform** - The probability of every candidate buzzer position is equal. This essentially means that our robot knows nothing about the buzzer's location.\n",
    "- **High-variance Gaussian** - Our robot has a rough clue that the buzzer should be near location $\\theta=0.5$ because that's where the peak of the belief is, but the high variance of the PDF means the robot is not so sure about its guess.\n",
    "- **Low-variance Gaussian** - Our robot has a fairly clear idea that the buzzer is around $\\theta=0.5$.\n",
    "\n",
    "Clearly, as we go from a uniform to low-variance Gaussian belief PDF, the robot gradually knows more about where the buzzer is. This gradual improvement can be quantified by measuring the entropy of the belief shown on the right panel. The entropy is highest with the uniform belief and gradually lowers as the variance lowers in the Gaussian case. The entropy of the belief provides a way for us to compare different beliefs in order to determine how good our current estimate is. The entropy of a belief is defined as\n",
    "$$\n",
    "S\\left[p(\\theta)\\right] = -\\sum_\\theta p(\\theta) \\log p(\\theta)\n",
    "$$\n",
    "where $p(\\theta)$ is the belief. We will use entropy reduction as the criterion for making decisions about search."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "L5lzE8xb0LWW"
   },
   "source": [
    "### Recursive Bayesian Filtering\n",
    "At this point, we have already defined:\n",
    "- **The Observation Model $\\Upsilon(\\theta, x)$**, which captures how the sensor responds as a function of the position of the target. \n",
    "- **The Likelihood Function $p(V~\\rvert~\\theta, x)$**, which quantifies where the target is likely to be given a specific measurement.\n",
    "- **The Belief $p(\\theta)$**, which encodes all the information we know about the target's location in the form of a probability density function.\n",
    "\n",
    "Let's say we begin with a uniform belief and let the robot take a measurement at its current location $x_0$. How do we use the likelihood function to update the belief? That's where the Bayesian filter kicks in:\n",
    "\n",
    "$$\n",
    "p(\\theta~\\rvert~V, x) = \\dfrac{p(V~\\rvert~\\theta, x)~p(\\theta)}{p(V~\\rvert~x)} = \\eta~p(V~\\rvert~\\theta, x)~p(\\theta)\n",
    "$$\n",
    "\n",
    "where $p(V~\\rvert~\\theta, x)$ is the likelihood function, $p(\\theta)$ is the prior belief (belief before update), $p(\\theta~\\rvert~V, x)$ is the posterior belief (belief after update), and $\\eta = \\frac{1}{p(V~\\rvert~x)} = \\frac{1}{\\int_{\\theta} p(V~\\rvert~\\theta,x)~p(\\theta)d\\theta}$ is a normalization factor that constrains the posterior belief $p(\\theta~\\rvert~V, x)$ to be a probability distribution. This equation shows how to update the belief using the likelihood function. We do this for each measurement."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "SQ_IFec3Ibzs"
   },
   "source": [
    "## 5. Expected Information Density\n",
    "\n",
    "At this point we know how to use sensor measurements to recursively update the belief. Do all sensor measurements have the same effect on our belief when used in the Bayesian filter? In other words, are all potential measurements equally informative? To answer this question, imagine two different scenarios where the robot potentially takes a measurement either at location $x=0$, or location $x=0.5$, yielding potential measurements $V_1$ and $V_2$, respectively. Based on a Gaussian prior belief $p(\\theta)$ centered at 0.5 and the observation model, we compute the expectation $V_1\\approx0$ and $V_2\\approx1$. \n",
    "\n",
    "This tells us that $V_1$ will likely indicate that \"the target is probably not here\" and $V_2$ will likely indicate that \"the target should be very close\". Which measurement yields more information about the location of the target—in other words, a better posterior belief with lower entropy? If we calculate the expected entropy reduction for all posible sensor locations, we have a way of deciding what the next sensor location should be, by extremizing entropy reduction."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "colab": {
     "autoexec": {
      "startup": false,
      "wait_interval": 0
     },
     "base_uri": "https://localhost:8080/",
     "height": 397
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 1014,
     "status": "ok",
     "timestamp": 1523997160095,
     "user": {
      "displayName": "Chen Chen",
      "photoUrl": "//lh6.googleusercontent.com/-WdjMoiJU9X8/AAAAAAAAAAI/AAAAAAAABR4/a7zNcVTHSAY/s50-c-k-no/photo.jpg",
      "userId": "106846184394987586128"
     },
     "user_tz": 300
    },
    "id": "7HK5fQxNPl6O",
    "outputId": "7d10bc01-d7b8-45d2-eb60-b69293188198"
   },
   "outputs": [
    {
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\n",
      "text/plain": [
       "<Figure size 864x1296 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot some PDF as example and their corresponding entropy\n",
    "priorP1 = norm.pdf(wsSamples,0.5,0.2) # Gaussian belief\n",
    "priorP1 /= priorP1.sum()\n",
    "\n",
    "_, (ax1, ax2, ax3) = plt.subplots(3, 1, figsize=(12, 18))\n",
    "ax1.plot(wsSamples, Pvtheta(0.0, 0.0), color='g', label=r'Likelihood $p(V_1=0.0~|~\\theta, x=0.0)$')\n",
    "ax1.plot(wsSamples, Pvtheta(1.0, 0.5), color='b', label=r'Likelihood $p(V_2=1.0~|~\\theta, x=0.5)$')\n",
    "ax1.set_xlabel(r'Candidate Buzzer Position ($x$)', fontsize=14)\n",
    "ax1.set_ylabel(r'Likelihood', fontsize=14)\n",
    "ax1.legend(fontsize=14, loc='best');\n",
    "\n",
    "ppP1 = priorP1 * Pvtheta(0.0, 0.0)\n",
    "ppP2 = priorP1 * Pvtheta(1.0, 0.5)\n",
    "ppP1 /= ppP1.sum()\n",
    "ppP2 /= ppP2.sum()\n",
    "\n",
    "ax2.plot(wsSamples, priorP1, color='r', label='Prior belief')\n",
    "ax2.plot(wsSamples, ppP1, color='g', label='Posterior given $V_1=0$')\n",
    "ax2.plot(wsSamples, ppP2, color='b', label='Posterior given $V_2=1$')\n",
    "ax2.set_xlabel(r'Candidate Buzzer Position ($x$)', fontsize=14)\n",
    "ax2.set_ylabel(r'Probability', fontsize=14)\n",
    "ax2.legend(fontsize=14, loc='best');\n",
    "\n",
    "ax3.barh([0,1,2], [entropy(priorP1), entropy(ppP1), entropy(ppP2)], height=0.4, \n",
    "        color=['r', 'g', 'b'])\n",
    "ax3.set_yticks([0, 1, 2])\n",
    "ax3.set_yticklabels(('Prior', 'Posterior after $V_1$', 'Posterior after $V_2$'), \n",
    "                   fontsize=12)\n",
    "ax3.invert_yaxis()\n",
    "ax3.set_xlabel(r'Entropy of Belief', fontsize=14);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "sjDSyjvwT2g9"
   },
   "source": [
    "Clearly, $V_2$ wins. The entropy of the posterior belief after getting measurement $V_2$ leads to a much lower entropy when compared to $V_1$. This example tells us two main messages:\n",
    "1. Not all measurements are equally informative. Some measurements are more informative than others because they rule out more of the potential locations of the target.\n",
    "2. Entropy of the belief can be used to evaluate how informative a measurement is, with an expectation of lower entropy after taking a measurement indicating that the measurement is correspondingly more informative.\n",
    "\n",
    "It definitely sounds silly to let the robot randomly sample the entire workspace. It also does not sound right for the robot to take a measurement at a fixed location no matter what. Given the current belief, is there any good strategy that can help the sensor predict which location could lead to more informative measurement? The answer is yes and it involves the use the expected entropy reduction to form an expected information density (EID) map."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "sjDSyjvwT2g9"
   },
   "source": [
    "### Computing the Expected Information Density\n",
    "\n",
    "Given $p(\\theta)$, we want to compute for each $x$ the expected amount of information anticipated as a result of visiting location $x$. Let's try to break this down step-by-step:\n",
    "\n",
    "1. Define observation model $\\Upsilon(\\theta,x)$, measurement $V = \\Upsilon(\\theta,x) + \\epsilon$ (note that the sensor does not know $\\theta$, the synthesis of each measurement is taken care of by the simulation, the sensor simply ask for a new measurement), and Gaussian likelihood function:\n",
    "    $$\n",
    "    p(V~\\rvert~\\theta, x) = \\frac{1}{\\sqrt{2\\pi}\\sigma} \\exp{\\left[-\\frac{(V-\\Upsilon(\\theta,x))^2}{2\\sigma^2}\\right]}\n",
    "    $$\n",
    "\n",
    "2. With a predicted distribution of measurements for each choice of $x$ from the likelihood function $p(V~\\rvert~\\theta,x)$, we then evaluate what the expected new posterior belief $p(\\theta~\\rvert~V,x)$ is if the sensor were to take a potential measurement at a given location $x$ in the workspace. For each choice of potential $x$ where a sensor measurement could be taken, the new posterior is computed by applying the Bayesian update rule.\n",
    "    $$\n",
    "    p(\\theta~\\rvert~V, x) = \\eta~p(V~\\rvert~\\theta, x)~p(\\theta)\n",
    "    $$\n",
    "    \n",
    "3. Given a posterior belief $p(\\theta~\\rvert~V, x)$ evaluated on a potential $V$ measured at a potential location $x$, the entropy reduction from the prior belief $p(\\theta)$ can be evaluated using:\n",
    "    $$\n",
    "    \\Delta \\text{S}(V, x) = \\text{S} \\left[ p(\\theta) \\right] - \\text{S} \\left[ p(\\theta~\\rvert~V, x) \\right]\n",
    "    $$\n",
    "    where $S\\left[ p(\\theta) \\right] \\in \\mathbb{R}^1$ and $S\\left[ p(\\theta) \\right] = - \\sum_{\\theta} p(\\theta)~\\log p(\\theta)$ is the Shannon-Weaver entropy of the prior belief $p(\\theta)$, while $S \\left[ p(\\theta~\\rvert~V, x) \\right]$ is the Shannon-Weaver entropy of the posterior belief.\n",
    "\n",
    "4. For any given prior belief $p(\\theta)$, the probability of the sensor receiving a measurement $V$ given a choice of sensing location $x$ is not necessarily constant. Therefore, to evaluate the expected entropy reduction at a given sensing location $x$, the entropy reduction $\\Delta S(V, x)$ needs to be weighted by the measurement probability $p(V~\\rvert~x)$ that is consistent with the prior belief $p(\\theta)$. This weighted probability can be obtained by applying the law of total probability to the normalized likelihood function $p(V~\\rvert~\\theta, x)$ treated as a probability distribution.\n",
    "\t$$\n",
    "\tp(V~\\rvert~x) = \\int_{\\theta} p(\\theta)p(V~\\rvert~\\theta, x) d\\theta\n",
    "\t$$\n",
    "\n",
    "5. Finally, the expected information density at location $x$&#151;$\\text{EID}(x)$&#151;is obtained by computing the mathematical expectation of the entropy reduction *if one were* to take a measurement at location $x$. That is, $\\text{EID}(x)$ is the weighted average entropy reduction resulting from the conditional probability $p(\\theta~\\rvert~V, x)$, weighted by the measurement probability $p(V~\\rvert~x)$.\n",
    "\t$$\n",
    "\t\\text{EID}(x) = \\text{E} \\left[ \\Delta S(x) \\right] = \\int_V p(V~\\rvert~x)~\\Delta S(V, x) dV\n",
    "\t$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To illustrate the calculation, we will show the EID for a given belief distribution $p(\\theta)$, in this case an imagined multi-peak distribution. Recall from the start of the tutorial that the sensor's measurement of sound loudness is denoted by $V \\in \\mathbb{V} = [0, 1]$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "colab": {
     "autoexec": {
      "startup": false,
      "wait_interval": 0
     },
     "base_uri": "https://localhost:8080/",
     "height": 701
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 800,
     "status": "ok",
     "timestamp": 1523991807212,
     "user": {
      "displayName": "Chen Chen",
      "photoUrl": "//lh6.googleusercontent.com/-WdjMoiJU9X8/AAAAAAAAAAI/AAAAAAAABR4/a7zNcVTHSAY/s50-c-k-no/photo.jpg",
      "userId": "106846184394987586128"
     },
     "user_tz": 300
    },
    "id": "zULzBtjd4kou",
    "outputId": "2958dacc-434d-4ac0-f7fc-48226cbbc86f"
   },
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 1008x432 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Construct an arbitrary complex prior belief\n",
    "priorP = norm.pdf(wsSamples,0.8,0.1) + \\\n",
    "         norm.pdf(wsSamples,0.3,0.1) + \\\n",
    "         norm.pdf(wsSamples,0.05,0.1) + \\\n",
    "         norm.pdf(wsSamples,0.6,0.15) \n",
    "priorP /= sum(priorP)\n",
    "\n",
    "\n",
    "# Compute likelihood Pvx\n",
    "def PvxNew(v, theta=wsSamples, prior=priorP, sigmaM=0.1, sigmaL=0.2):\n",
    "    pL = Pvtheta(v, theta, sigmaM, sigmaL)\n",
    "    pvx = pL\n",
    "    for idx in range(pvx.shape[0]):\n",
    "        pvx[idx, :] = pvx[idx, :] * prior[idx]\n",
    "    pvx = pvx.sum(axis=0)\n",
    "    return pvx, pL\n",
    "\n",
    "fig, ax1 = plt.subplots(figsize=(14,6))\n",
    "ax2 = ax1.twinx()\n",
    "h1 = ax1.plot(wsSamples, PvxNew(0.1)[0], label='Measurement Probability ($V=0.1$)', color='r')\n",
    "h2 = ax2.plot(wsSamples, priorP, label='Prior Belief')\n",
    "h = h1 + h2\n",
    "lbl = [l.get_label() for l in h]\n",
    "plt.title(r\"Prior belief $p(\\theta)$ and measurement probability $p(V=0.1~|~x)$\", fontsize=16)\n",
    "ax1.set_xlabel(\"Position ($x$)\", fontsize=16)\n",
    "ax1.set_ylabel(\"Prior Probability\", fontsize=16)\n",
    "ax2.set_ylabel(\"Measurement Probability\", fontsize=16, color='r')\n",
    "plt.legend(h, lbl, fontsize=12);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Test your understanding: What should the measurement probability look like for $V=0.9$? Change `PvxNew(0.1)` to `PvxNew(0.9)` at line 20 in the block above and see if you are correct."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "colab": {
     "autoexec": {
      "startup": false,
      "wait_interval": 0
     },
     "base_uri": "https://localhost:8080/",
     "height": 447
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 2203,
     "status": "ok",
     "timestamp": 1523991985412,
     "user": {
      "displayName": "Chen Chen",
      "photoUrl": "//lh6.googleusercontent.com/-WdjMoiJU9X8/AAAAAAAAAAI/AAAAAAAABR4/a7zNcVTHSAY/s50-c-k-no/photo.jpg",
      "userId": "106846184394987586128"
     },
     "user_tz": 300
    },
    "id": "LJTn1DKK4koy",
    "outputId": "05e7e6b6-6ebb-4e16-ba6e-3f25d8f48f72"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Maximum possible entropy = 4.6151205168412615\n",
      "Entropy of current prior = 4.570760331054973\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1008x432 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Construct EER function\n",
    "def EER(prior, sigmaM=0.1, sigmaL=0.2):\n",
    "    sBase = entropy(prior)\n",
    "    deltaS = np.zeros(wsResolution)\n",
    "    for mms in np.linspace(0,1,wsResolution):\n",
    "        # Posterior\n",
    "        pvx, pL = PvxNew(v=mms, prior=prior, sigmaM=sigmaM, sigmaL=sigmaL)\n",
    "        pp = pL * prior\n",
    "        # Entropy\n",
    "        dS = sBase - entropy(pp.T)\n",
    "        # Update result\n",
    "        deltaS += pvx * dS\n",
    "    # Convert deltaS to Entropy EID\n",
    "    EER_Entropy = deltaS\n",
    "    EER_Entropy[EER_Entropy == np.inf] = 0\n",
    "    EER_Entropy[EER_Entropy < 0] = 0\n",
    "    if abs(EER_Entropy).sum() != 0:\n",
    "        EER_Entropy /= EER_Entropy.sum()\n",
    "    \n",
    "    return EER_Entropy\n",
    "\n",
    "# Compute base entropy\n",
    "sMax = entropy(np.ones(wsResolution)/wsResolution)\n",
    "sBase = entropy(priorP)\n",
    "print(\"Maximum possible entropy = {0}\".format(sMax))\n",
    "print(\"Entropy of current prior = {0}\".format(sBase))\n",
    "\n",
    "# Compute EER map\n",
    "EER_Entropy = EER(priorP)\n",
    "\n",
    "# Plot entropy map\n",
    "# plt.figure(figsize=(14,6))\n",
    "fig, ax1 = plt.subplots(figsize=(14,6))\n",
    "ax2 = ax1.twinx()\n",
    "h1 = ax1.plot(wsSamples, EER_Entropy, label='EID', color='r')\n",
    "h2 = ax2.plot(wsSamples, priorP, label='Prior Belief')\n",
    "h = h1 + h2\n",
    "lbl = [l.get_label() for l in h]\n",
    "plt.title(r\"EID(s) = E$\\left[ \\Delta S(x) \\right]$, and prior belief $p(\\theta)$\", fontsize=16)\n",
    "ax1.set_xlabel(\"Position ($x$)\", fontsize=16)\n",
    "ax1.set_ylabel(\"Probability\", fontsize=16)\n",
    "ax2.set_ylabel(\"EID\", fontsize=16, color='r')\n",
    "plt.legend(h, lbl, fontsize=12);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Evaluating the EID for the shown belief, we can see the expected amount of information for every candidate sensing location in the workspace. Note that the EID indicates that a measurement at $x$ near 0.15 is probably the next best place to take a measurement while $x$ near 0.8 is also a good choice (and might be more convenient depending on the current state $x$)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "FFH-wp-64ko1"
   },
   "source": [
    "### Example EID on Different Beliefs"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Below, we show EID on 6 different belief distributions including flat, unimodal, and multi-modal distributions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "autoexec": {
      "startup": false,
      "wait_interval": 0
     },
     "base_uri": "https://localhost:8080/",
     "height": 825
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 11625,
     "status": "ok",
     "timestamp": 1519231104937,
     "user": {
      "displayName": "chenchen2015",
      "photoUrl": "https://lh3.googleusercontent.com/a/default-user=s128",
      "userId": "105669591793905724503"
     },
     "user_tz": 360
    },
    "id": "as0SsHgL4ko2",
    "outputId": "c14aec8b-dc80-4904-c0b3-dd43e9637c0a"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Prior example 1 - flat - entropy = 4.6151205168412615\n",
      "Prior example 2 - Reciprocal inverse Gaussian, low variance - entropy = 3.4031070758599844\n",
      "Prior example 3 - Unimodal, centered, high variance - entropy = 4.361006466387932\n",
      "Prior example 4 - Unimodal, cornered, low variance - entropy = 3.61616276953873\n"
     ]
    }
   ],
   "source": [
    "## Construct a variety of different prior beliefs and compute the corresponding EID maps\n",
    "priorP1 = np.ones(wsResolution)/wsResolution  # Flat belief\n",
    "EID_Entropy1 = EER(priorP1)\n",
    "print(\"Prior example 1 - flat - entropy = {0}\".format(entropy(priorP1)))\n",
    "\n",
    "priorP2 = recipinvgauss.pdf(wsSamples+1e-4,0.6,0,0.05)  # Reciprocal inverse Gaussian, centered, low variance\n",
    "priorP2 /= priorP2.sum()\n",
    "EID_Entropy2 = EER(priorP2)\n",
    "print(\"Prior example 2 - Reciprocal inverse Gaussian, low variance - entropy = {0}\".format(entropy(priorP2)))\n",
    "\n",
    "priorP3 = norm.pdf(wsSamples,0.5,0.2)  # Unimodal, centered, high variance\n",
    "priorP3 /= priorP3.sum()\n",
    "EID_Entropy3 = EER(priorP3)\n",
    "print(\"Prior example 3 - Unimodal, centered, high variance - entropy = {0}\".format(entropy(priorP3)))\n",
    "\n",
    "priorP4 = norm.pdf(wsSamples,0.5,0.09)  # Unimodal, centered, low variance\n",
    "priorP4 /= priorP4.sum()\n",
    "EID_Entropy4 = EER(priorP4)\n",
    "print(\"Prior example 4 - Unimodal, cornered, low variance - entropy = {0}\".format(entropy(priorP4)))\n",
    "\n",
    "priorP5 = norm.pdf(wsSamples,0.7,0.12) + norm.pdf(wsSamples,0.3,0.12) # Bimodal, centered, high variance\n",
    "priorP5 /= priorP5.sum()\n",
    "EID_Entropy5 = EER(priorP5)\n",
    "print(\"Prior example 5 - Bimodal, centered, high variance - entropy = {0}\".format(entropy(priorP5)))\n",
    "\n",
    "priorP6 = norm.pdf(wsSamples,0.7,0.06) + norm.pdf(wsSamples,0.3,0.06) # Bimodal, centered, high variance\n",
    "priorP6 /= priorP6.sum()\n",
    "EID_Entropy6 = EER(priorP6)\n",
    "print(\"Prior example 6 - Bimodal, centered, low variance - entropy = {0}\".format(entropy(priorP6)))\n",
    "   \n",
    "# Build data list\n",
    "priorList = [priorP1, priorP2, priorP3, priorP4, priorP5, priorP6]\n",
    "EIDList = [EID_Entropy1, EID_Entropy2, EID_Entropy3, EID_Entropy4, EID_Entropy5, EID_Entropy6]\n",
    "\n",
    "## Compare Entropy and Fisher Information on Different Priors\n",
    "f, axArray = plt.subplots(3, 2, sharex='col', figsize=(15, 12))\n",
    "axArray = axArray.flatten()\n",
    "for idx, p in enumerate(priorList):\n",
    "    axArray[idx].plot(wsSamples, EIDList[idx], label='EID')\n",
    "    axArray[idx].plot(wsSamples, p, label='Prior Belief')\n",
    "    axArray[idx].set_xlabel(\"Position\", fontsize=14)\n",
    "    axArray[idx].set_ylabel(\"EID\", fontsize=14)\n",
    "    axArray[idx].legend(fontsize=12, loc='best');"
   ]
  }
 ],
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